Adoption of Managerial Decisions for a Small Number of Input Data

Abstract

Existing methods of statistical analysis of data and the registration of a small number of observations or tests lead to the need for an organization unnecessarily large number of experiments. In case of the impossibility of conducting the required number of experiments, the results of the analysis are insufficiently reliable. In this paper, statistical methods of increasing the efficiency of processing a small number of experiments and observations for the adoption of sound managerial decisions and the use of appropriate corrective actions are considered. The method of calculating the mathematical expectation and dispersion of the error of construction of the integral distribution law (IDL) based on the method of compression of the region of its existence, as well as the construction of the corresponding nomograms for solving a large number of practical tasks of object management, processes, research and testing is proposed. In the described method of compression of the area of the existence of IDL to consider a priori, the whole set of possible IDLs is introduced. This translates the analysis from a two-dimensional to three-dimensional probability space by introducing concepts such as the probability density of IRAs, probably as a model of a population of IARs that changes after the registration of the results of each subsequent experiment, the section of the probability, and some others. The analysis made it possible to detect the objectively existing area of a small number of tests and specify the number of tests required to obtain the desired result. Compared with the estimates obtained from the inequality of PL Chebyshev, the required number of tests can be reduced in 2% times and at least 4 times in the analysis of the variance of the error of constructing the IDR. Based on the results obtained, new convergence criteria are introduced which begin to work with n = 3.